**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30174

##### An Improved Learning Algorithm based on the Conjugate Gradient Method for Back Propagation Neural Networks

**Authors:**
N. M. Nawi,
M. R. Ransing,
R. S. Ransing

**Abstract:**

**Keywords:**
Back-propagation,
activation function,
conjugategradient,
search direction,
gain variation.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1328444

**References:**

[1] D.E. Rumelhart, G.E. Hinton, and R.J. Williams, Learning internal representations by error propagation. in D.E. Rumelhart and J.L. McClelland (eds), Parallel Distributed Processing, 1986. 1: p. 318- 362.

[2] Marco Gori and Alberto Tesi, On the problem of local minima in back-propagation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992. 14(1): p. 76-86.

[3] E.K. Blum, Approximation of Boolean functions by sigmoidal networks: Part I: XOR and other two-variable functions. Neural Computation, 1989. 1(4): p. 532-540.

[4] A. van Ooyen and B. Nienhuis, Improving the convergence of the back-propagation algorithm. Neural Networks, 1992. 5: p. 465-471.

[5] M. Ahmad and F.M.A. Salam, Supervised learning using the cauchy energy function. International Conference on Fuzzy Logic and Neural Networks, 1992.

[6] Pravin Chandra and Yogesh Singh, An activation function adapting training algorithm for sigmoidal feedforward networks. Neurocomputing, 2004. 61: p. 429-437.

[7] R.A. Jacobs, Increased rates of convergence through learning rate adaptation. Neural Networks, 1988. 1: p. 295-307.

[8] M. K. Weir, A method for self-determination of adaptive learning rates in back propagation. Neural Networks, 1991. 4: p. 371-379.

[9] X. H. Yu, G.A. Chen, and S.X. Cheng, Acceleration of backpropagation learning using optimized learning rate and momentum. Electronics Letters, 1993. 29(14): p. 1288-1289.

[10] Bishop C. M., Neural Networks for Pattern Recognition. 1995: Oxford University Press.

[11] R. Fletcher and M. J. D. Powell, A rapidly convergent descent method for nlinimization. British Computer J., 1963: p. 163-168.

[12] Fletcher R. and Reeves R. M., Function minimization by conjugate gradients. Comput. J., 1964. 7(2): p. 149-160.

[13] M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systerns. J. Research NBS, 1952. 49: p. 409.

[14] Huang H.Y., A unified approach to quadratically convergent algorithms for function minimization. J. Optim. Theory Appl., 1970. 5: p. 405-423.

[15] Thimm G., Moerland F., and Emile Fiesler, The Interchangeability of Learning Rate an Gain in Back propagation Neural Networks. Neural Computation, 1996. 8(2): p. 451-460.

[16] Holger R. M. and Graeme C. D., The Effect of Internal Parameters and Geometry on the Performance of Back-Propagation Neural Networks. Environmental Modeling and Software, 1998. 13(1): p. 193-209.

[17] Eom K. and Jung K., Performance Improvement of Back propagation algorithm by automatic activation function gain tuning using fuzzy logic. Neurocomputing, 2003. 50: p. 439-460.

[18] Rumelhart D. E., Hinton G. E., and Williams R. J., Learning internal representations by back-propagation errors. Parallel Distributed Processing, 1986. 1 (Rumelhart D.E. et al. Eds.): p. 318-362.

[19] L. Prechelt, Proben1 - A set of Neural Network Bencmark Problems and Benchmarking Rules. Technical Report 21/94, 1994: p. 1-38.

[20] Fisher R.A., The use of multiple measurements in taxonomic problems. Annals of Eugenics, 1936. 7: p. 179 -188.

[21] Erik Hjelmas and P.W. Munro, A comment on parity problem. Technical Report, 1999: p. 1-7.

[22] Mangasarian O. L. and W.W. H., Cancer diagnosis via linear programming. SIAM News, 1990. 23(5): p. 1-18.

[23] Lutz Prechelt, ftp://ftp.ira.uka.de/pub/neuron/proben1.tar.gz. 1994.

[24] R. A. Fisher, ftp://ftp.ics.uci.edu/pub/machinelearningdatabases/ iris/iris.data. 1988.